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2020 Two integral transformations related to $\zeta(2)$
Raffaele Marcovecchio
Mosc. J. Comb. Number Theory 9(4): 441-452 (2020). DOI: 10.2140/moscow.2020.9.441

Abstract

We prove two integral transformations that relate different constructions of rational approximations to ζ(2). The first one relates a double integral over the unit square and a Barnes-type integral. The second one relates two Barnes-type integrals and was discovered and proved by W. Zudilin using an automated proof method. Here we offer a proof based on more classical means such as contiguous relations, the second Barnes lemma and the duplication formula for the gamma function.

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Raffaele Marcovecchio. "Two integral transformations related to $\zeta(2)$." Mosc. J. Comb. Number Theory 9 (4) 441 - 452, 2020. https://doi.org/10.2140/moscow.2020.9.441

Information

Received: 31 December 2019; Accepted: 5 May 2020; Published: 2020
First available in Project Euclid: 12 November 2020

zbMATH: 07272361
MathSciNet: MR4170708
Digital Object Identifier: 10.2140/moscow.2020.9.441

Subjects:
Primary: 11J82
Secondary: 33C20, 33C60

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 4 • 2020
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